Ductile Materials under Combined Stress. 81 



invariable and essential to the manufacture of a uniform 

 material, and that annealing seems usually to remove this 

 state of set. In the results of the tests shown, it will appear, 

 at any rate so far as the occurrence of the yield-point was 

 concerned, that the materials were practically isotropic. 



In the case of experiments upon wires, which after anneal- 

 ing show a marked want o£ isotropy, it is probably due to 

 overdrawing in the manufacture of the wire, which produces 

 a series of conical defects along the wire, the effect of which 

 evidently could not be removed by annealing. Unless the 

 wire is wanted particularly hard for some special purpose, 

 this defect is not likely to occur. 



23. Objection to Tubes on account of large effect of defects. — 

 Another objection, which can well be raised to the use of such 

 thin-walled tubes as those which I experimented upon, is the 

 large effect which would be produced by variations and 

 defects in the specimen, especially in the torsion experiments. 

 The tubes were all carefully examined before use, and none 

 showing visible defects were employed ; the greatest variation 

 in external diameter was about - 005 inch in l - 25 inch. This 

 examination was intended, however, merely to avoid the waste 

 of time which the testing of an obviously poor specimen would 

 involve. 



If any flaw existed in the material, or i£ the surfaces were 

 not close approximations to concentric circular cylinders, the 

 values of the elastic constants would be considerably changed, 

 and always to a lower value ; the density of the material 

 would be low ; and the stress- strain curve would soon cease 

 to be straight. 



Now in all the tests measurements of the distortions pro- 

 duced, as well as of the forces applied, were taken. The 

 moduli of rigidity and extension calculated from these were 

 never found to be widely different from their customary value, 

 and especially they are never low in value. (See Table I.) 

 Also the densities found were high. Furthermore, the stress- 

 strain curves to within a point not far below the yield-point 

 were always found to be straight. 



24. The System of Tests. — The method of experimenting em- 

 ployed was, then, to subject the tubes to torque, to torque and 

 tension combined, to tension only, to tension and internal pres- 

 sure combined, to torsion and internal pressure combined, and 

 to internal pressure only ; and to take measurements of the 

 axial elongation, of the twist when torque was employed, and 

 in some cases of the circumferential strain. The range of 

 the two principal stresses thus covered was from — p, +p to 

 +p, +p, the third principal stress being small, or zero. 

 Phil. Mag. S. 5. Vol. 50. No. 302. July 1900. G 



